I think there's a difference between someone who is left, and someone who is a leftist. Leftist tends to be used to label communists and socialists, where "the left" generally includes progressives, social democrats, and so on. It's a pretty subjective concept though and easy to split hairs on. You could reasonably call Obama or Clinton centrists.
I think Obama's campaign rhetoric would have been in line with the British Labour Party, but his actual policies were definitely moderate conservative. Probably similar to Cameron.